Unfortunately Yuling‘s talk already happened but the abstract is so intriguing I had to share it with you:

The standard paradigm of Bayesian statistics starts by “Let there be a joint distribution”. But was there a joint distribution? The premise on the joint distribution over data and parameters is at best artificial: Latent variables don’t always exist; The model is almost always wrong hence the assumption of a true fixed parameter is not meaningful; Leaving a particular observation unmeasured is not always the same as treating it as uncertain in a joint distribution. A safer view is to only recognize the likelihood as a sequence of explanations of data. To this end, I propose a general probabilistic inference paradigm formulated from a larger encompassing model that includes individual sampling model as special cases, where the familiar Bayes is recovered when such operator is chosen to be a mixture. Mixtures play a key role in Bayesian inference: The posterior predictive distribution is always a mixture of sampling distribution. I will discuss other alternative operators, such as convolution, geometric bridge, and quantum superposition—To better understand the additive model, we shall first understand what the addition operator is.